What is Probability ?
Computation of the chance of an occurrence of a certain event is called probability. Hence, probability is the study of random happening of an event and uncertainty, e.g. “Probability of rain tomorrow is only 35%”, and “Probability of winning a lottery is 1 out of 40,406,353”.
Before conducting an experiment, the absolute certainty of the outcome is unpredictable, therefore it is termed as probability, which actually depends on the idea of a random experiment’.
The theory of probability originates from the ‘game of chance’ associated with gambling, e.g., consider a game like gambling, tossing of a coin, throwing of a die, and random drawing of cards from a pack of cards. Thus, in statistics, probability (of an event) is defined as the ‘proportion of time’ in which an event occurs and is observed, even if the experiment is run an infinite number of times.
Contents :
- Meaning and Definition of Probability.
- General Rule for Probability.
- Application of Probability.
- Characteristics of Probability Function P(A).
- Uses of Probability in Decision Making.
- Types of Probability : Objective Probability & Subjective Probability Theory.
Meaning and Definition of Probability :
Probability is the mode of expression of knowledge or belief whether the event has occured or will occur. Thus, in the theory of probability this concept has been given an exact mathematical significance for being used widely in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy, so that conclusions can be drawn regarding the probability of potential events and the mechanics of complex systems being hidden.
According to Levin :
“We live in a world in which we are unable to forecast the future with complete certainty. Our need to cope with uncertainty leads us to the study and use of probability theory“.
According to American Heritage Dictionary :
“Probability is the branch of mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of a defined system”.
General Rule for Probability :
The probability of an event (say A) is defined as follows :
If an event happens m times and it fails n times, then the probability (p) of event A is defined as :
m
P(A) = ——–
m+n
The number of cases favorable to
the occurence of the event
P(A) = ————————————————
Total number of mutually exclusive
and exhaustive cases
So the total number of trials favorable to the event (A) divided by the total number of ways in which the event (A) can happen.
The number of cases favorable to
the occurence of the event
P(A) = ————————————————-
Total number of mutually exclusive
and exhaustive cases
Probability in favor of the occurrence of the event :
The number of cases favorable to
m the occurence of the event
— = —————————————————
n The number of cases against
the occurrence of the event
Probability against the occurrence of the event :
The number of cases against
n the occurence of the event
— = ————————————————
m The number of cases favorable to
the occurrence of the event
Applications of Probability :
- It plays a great role in making predictions.
- It is used to solve scientific investigations as well as day-to-day problems.
- It is very useful when one wants to predict the uncertainties of betting.and chances of success.
- It is extensively used in business and economics.
- It is the basis of the law of statistical regularity and law of inertia of a large number.
Characteristics of Probability Function P(A) :
- The limit of probability of an event A is between 0 and 1, i.e. 0<P(A)<1.
- When probability of two events A and B which are mutually exclusive, is combined, the probability is the sum of individual probabilities of A and B, i.e., P(AOB) will be P (A) + P (B).
- Two events which are equivalent are assigned the same probability.
Uses of Probability in Decision-Making :
Following are the business situations where managers use probability to take a decision :
1) Investment Problem :
A company’s manager has two different projects (with different initial costs) for investment. The decision taken by the manager is based on the choice that the outcome of which is dependent on the level of demand.
2) Introducing a New Product :
While introducing a new product there arises a problem in deciding about the introduction of the product. The decision maker is not sure whether the product would be acceptable or not. Hence after conducting test, marketing in three different regions the results being contradictory, the idea of introducing a new product should be dropped ? Thus, it is necessary to answer this question : what would be the chances of success of introducing a new product ?.
3) Stocking Decisions :
The demand of a perishable commodity is unknown to its dealer in advance. Thus if the commodity is not sold by the end of the day it will be spoiled. Therefore, he is not sure about the demand pattern and stock amount (that how much commodity is to be stored in advance).
4) The Individual Investor :
Maximisatiorn of returns is the motive of investors who are engaged in buying and selling of equities. The behavior of equities/ security prices is uncertain and it depends upon various factors. In this situation, managers take decisions on the basis of their prediction about future prices of the securities. This prediction helps the investor to take a decision as to which.securities he/she should select for the investment.